Diffusion MRI combines the physics of diffusion and the physics of MRI to enable the measurement of the displacement of water molecules in the brain. The spin echo effect discovered by Rewin Hanhn in 1950 and the subsequent mathematical and physical framework introduced by Carr and Purcell in 1954 opened up the possibility of measuring the diffusion coefficient of spin-labeled molecules. A few years later, Stejskal and Tanner introduced the pulsed gradient spin echo (PGSE) sequence based on the addition of a pair of bipolar magnetic field gradients to a spin echo sequence, to sensitize the MR signal to the diffusion of water molecules [173]. In this formalism, the diffusion coefficient D in a given direction can be measured using two MR acquisitions: a diffusion-weighted acquisition with a pair of diffusion-encoding gradients oriented in the direction and a baseline acquisition with the diffusion-encoding gradients set to zero. The signal intensity attenuation resulting from the application of the diffusion-encoding gradients is given by the equation:
where S ₀ is the signal intensity of the baseline acquisition, b is the diffusion-weighting factor, and D is the diffusion coefficient. The diffusion-weighting factor, or so-called b-value, is calculated based on the amplitude of the magnetic field gradient pulses G, their duration δ and temporal separation ∆, and the gyromagnetic ratio of hydrogen γ:

From Eq. (20.2), the apparent diffusion coefficient in the encoding direction is expressed as:

Since ADC values depend on the direction, diffusion-weighted imaging data are usually acquired sequentially using three or more orthogonal diffusion-encoding gradient directions and the measurements are averaged to obtain mean ADC values at each voxel.

In neuro-oncology imaging, ADC maps can be used to investigate pathological changes and monitor treatment [3]. The quantitative information provided by ADC maps can be complementary to invasive histopathology of tissue biopsy samples, which is the current gold standard for distinguishing among gliomas subtypes. However, ADC measurements cannot be used to diagnose a particular tumor due to the overlap between the tumor-specific ranges of diffusion values [4]. During treatment monitoring, the evaluation of changes in tumor ADC values before and after initiation of chemotherapy and radiation therapy has been investigated as a potential indicator of early tumor response [5, 6]. Such non-invasive quantitative imaging biomarker could aid physicians individualize treatment, minimize unnecessary systemic toxicity associated with ineffective therapies, and gain precious time [7, 8].

Diffusion MRI pulse sequences use long and strong diffusion-encoding gradients that make the acquisitions very sensitive to involuntary patient movement, respiratory motion, and cardiac pulsation. Motion-corrupted diffusion weighted imaging (DWI) datasets can present ghosting artifacts and heterogeneous misregistration errors. A second major source of artifacts arises from eddy currents induced by the rapid switching of the diffusion-encoding gradient pulses. Eddy currents generate local magnetic field gradients that get combined with the diffusion-encoding gradients and result in ghosting artifacts that can lead to misinterpretation of the DWI scans. Finally, Echo Planar Imaging (EPI) sequences, the most commonly used diffusion MRI sequences in the clinics, are very sensitive to inhomogeneities of the static magnetic field B ₀. These inhomogeneities produce EPI geometric distortion that can be important at the interface between bones and air-filled cavities, such as the sinuses and the auditory canal, as well as at the interface between brain tissues and air during intra-operative MRI acquisition.

Numerous techniques exist to prevent the apparition of image artifacts during the acquisition of DWI scans. These techniques include cardiac gating and head holders for motion-related artifacts, self-shielded gradient coils and proper calibration for eddy-current artifacts, as well as maps of the static magnetic fields and blip-up blip-down acquisitions for EPI distortion [9, 10]. Once a DWI scan is acquired, quality control of the raw images is an essential step before starting any post-processing pipeline. While visual inspection of each diffusion-weighted image can provide a quick detection of acquisition artifacts, the process is time-consuming and operator-dependent. In addition, image misalignment caused by patient motion across scans can be difficult to detect [11]. To overcome these limitations, several tools for quality control and automated artifacts correction of DWI data have been developed by the diffusion MRI research community. Most of these tools are available as open-source software packages, and provide useful resources to minimize the impact of artifacts encountered during clinical diffusion MRI acquisition [9, 12–14].

The diffusion of water molecules in the brain is sensitive to the underlying tissue microstructures [1]. In gray matter and cerebrospinal fluid, the displacement of water molecules is identical in all directions and the diffusion is isotropic. In white matter fibers, as myelin sheets and axonal membranes act as barriers, the displacement of water molecules is less hindered in the direction parallel to the fibers than in the direction perpendicular to their axis, and thus the diffusion is anisotropic [15]. Diffusion Tensor Imaging (DTI) was the first mathematical framework introduced to model the anisotropic diffusion of water molecules in the brain [174]. In the tensor model, the signal attenuation S _k resulting from the application of the diffusion-encoding gradient in the direction is expressed at each voxel as:
where S ₀ is the signal intensity of the baseline acquisition, b is the diffusion-weighting factor, D is the diffusion tensor and is the unit vector describing the diffusion-encoding direction. The diffusion tensor D is a 3 × 3 symmetric matrix defined by six elements. Thus, a minimum of six diffusion-weighted acquisitions with six diffusion-encoding gradients oriented in non-colinear and non-coplanar directions is necessary to compute the tensor elements at each voxel. The diffusion tensor is then diagonalized to compute the three principal directions (), called eigenvectors, and the three diffusion coefficients (λ ₁, λ ₂, λ ₃), called eigenvalues. The eigenvalues correspond to the apparent diffusivities along the eigenvectors, and the eigenvector associated with the largest eigenvalue corresponds to the direction of maximum diffusion. The eigenvectors and eigenvalues are rotationally independent, thereby DTI volumes are intrinsic to the brain structures being imaged, and are independent of both the orientation of the diffusion-encoding gradients used for the acquisition and the orientation of the patient in the MR scanner coordinate system.

Diffusion tensors can be represented using small graphical objects called glyphs in the shape of an ellipsoid. The diffusion tensor ellipsoid represents the isoprobability surface where a molecule of water placed at its center will diffuse [16, 17]. The axes of the diffusion tensor ellipsoid correspond to the eigenvectors and the length of the axes are proportional to the square root of the eigenvalues. The shape of the ellipsoid provides an intuitive visualization of the diffusion properties of different tissues: in anisotropic media, the diffusion tensor glyphs are either cigar-shaped or disk-shaped, while in isotropic media the glyphs are spherical. Color schemes were subsequently introduced to represent fiber direction from DTI data [18]. In directionally encoded color (DEC) images, white matter fibers oriented in the left-right direction appear red; fibers oriented in the anterior-posterior direction appear green; and fibers oriented in the superior-inferior direction appear blue. Through this representation, DEC maps derived from DTI data enable an intuitive identification of all major white matter association, commissural and projection pathways of the human brain.

In addition to the visual display of white matter fiber orientation, quantitative scalar parameters that measure different intrinsic features of anisotropic tissues can be computed from DTI data [17]. The most commonly used metrics are the mean diffusivity (MD), which is a measure of the amplitude of water diffusion, and the fractional anisotropy (FA), which quantifies the degree of anisotropy of diffusion, with values ranging between FA = 0.0 in isotropic media and FA = 1.0 in highly anisotropic tissue. Figure 20.1 shows an example of FA map, DEC map and diffusion tensor glyphs.

Quantitative DTI data enable non-invasive evaluation of microstructural and physiological features of tissues [19]. Exploratory studies have investigated the use of DTI-derived metrics for the detection of peritumoral white matter infiltration in low-grade and high-grade gliomas [20–23] and the characterization of microstructural integrity in meningiomas and low-grade gliomas [24]. These preliminary findings suggest a potential role for quantitative DTI in the detection of tumor infiltration in regions that appear normal on conventional MR imaging, which could provide neurosurgeons clinically relevant information on tumor margins of DLGG as tumor cells extend beyond radiological borders on FLAIR and T2-weighted images [25].

Diffusion Tensor Imaging provides an unprecedented opportunity to gain insights into the architecture of the human brain in vivo. While the tensor model provides a good estimate of fiber orientation in voxels where a single population of fibers exists, the model fails to characterize the diffusion in areas where fibers cross, bend, or fan. Modeling the diffusion of water in regions with complex fiber patterns is an active area of research, and numerous approaches have been developed in the past decade. These approaches can be broadly divided into two categories: model-based approaches and non-parametric algorithms [26].

Model-based approaches operate on a mathematical representation of the diffusion-weighted MR signal. Among these approaches are the multi-tensor models that represent the diffusion using a mixture of Gaussians, each representing a fiber population described by a single tensor model [26]. A constrained version of the multi-compartment model is the ball-and-stick model that decomposes the diffusion signal into an isotropic “ball” compartment and a number of completely anisotropic “stick” compartments [27]. Figure 20.2 shows examples of fiber crossings identified by the ball-and-stick model at the intersection between the pyramidal pathway and cerebellar tracts, and between the corona radiata and the superior longitudinal fasciculus. While the ball-and-stick model provides an elegant depiction of crossing fibers, the approach considers only a discrete set of fibers orientations and does not represent the orientation dispersion within the fiber bundles. The ball-and-rackets model was subsequently introduced to overcome this limitation and represent fanning geometries [28]. Other models such as the composite hindered and restricted model of diffusion (CHARMED) attempt at providing a physical description of the diffusion process in terms of hindered diffusion in the extra-axonal volume and restricted diffusion in the intra-axonal volume [29].

Non-parametric methods make no prior assumption on the molecular diffusion in a given voxel, and proceed by estimating the diffusion function directly. Such approaches include diffusion spectrum imaging (DSI) and q-ball imaging. DSI measures the diffusion function directly by sampling the diffusion signal on a three-dimensional Cartesian lattice [30]. In practice, DSI requires the acquisition of several hundred images and time-intensive sampling which are not compatible with clinical constraints. High angular resolution diffusion imaging (HARDI) sequences have been introduced as an alternative approach based on sampling in a spherical shell instead of a three-dimensional Cartesian volume [31]. The subsequent development of q-ball imaging, a model-independent reconstruction scheme for HARDI data, has enabled the depiction of fiber crossings both in deep white matter pathways and at the subcortical margin [32]. Q-ball imaging computes a probability distribution on the sphere known as the diffusion orientation distribution function (dODF), and peaks in dODF are assumed to correspond to fiber orientations [32]. The computation of ODF initially performed using the Funk-Radon transform has been simplified using spherical harmonics [33]. Other approaches include spherical deconvolution methods that recover an estimate of the fiber orientation distribution function (fODF) [34], diffusion orientation transform (DOT) that calculates a variant of the dODF [35], and persistent angular structure MRI (PAS-MRI) that models the relative mobility of water molecules in each direction [36].

In addition to the multitude of sophisticated model-based methods and non-parametric algorithms for recovering multiple fiber orientations from diffusion-weighted images, novel approaches have recently been developed to estimate the microstructural complexity of dendrites and axons from clinical data. These approaches include neurite orientation dispersion and density imaging (NODDI) and multi-compartment microscopic diffusion imaging based on the spherical mean technique (SMT). NODDI use a tissue model that distinguishes three types of microstructural environment: intra-cellular, extra-cellular, and cerebrospinal fluid compartments [37, 38]. Multi-compartment microscopic diffusion imaging maps the neurite density and compartment-specific microscopic diffusivities unconfounded by the effects of fiber crossings and orientation dispersion [39]. Such novel tools have the potential for providing new quantitative imaging biomarkers for the evaluation of complex tissues compositions associated with the progression of DLGG. A preliminary study on the feasibility of using multi-band diffusion weighted imaging data acquired at 7.0 Tesla to characterize gliomas has demonstrated the potential role of NODDI maps to provide a unique contrast within the tumor that is not visible in anatomical and DTI data [40].

Diffusion MRI tractography provides a geometrical representation of the trajectory of white matter pathways in the human brain. The first tractography algorithms introduced in the late nineties reconstructed the trajectory of water molecules based on the assumption that the main eigenvector of the diffusion tensor is parallel to the principal fiber orientation at each voxel [42, 176]. Numerous fiber tracking techniques have since been developed and tractography algorithms can be divided into four categories: deterministic, probabilistic, global, and filtered. Deterministic tractography propagates a streamline until a termination criteria is reached. The initial fiber assignment by continuous tracking (FACT) algorithm uses a linear propagation approach [41]. Starting from a seed point, the technique consists in propagating a line by following the orientation of the main eigenvector of the diffusion tensor until a termination criteria based on an anisotropy threshold or a local tract curvature is reached [42]. The FACT approach has demonstrated anatomically faithful reconstructions of white matter pathways in voxels containing anisotropic fibrous tissues presenting with a single fiber orientation. However, in areas containing two or more distinct fiber populations, the diffusion tensor fails to accurately represent the orientation of the underlying white matter anatomy, leading to inaccurate tractography reconstructions. While the subsequent development of the tensor deflection (TEND) approach using the entire diffusion tensor has shown improved performance in fiber crossing regions, the algorithm underestimates the trajectory curvature for curved pathways [43]. In addition, both FACT and TEND algorithms propagate of a streamline based solely on the local diffusion information. Thus, a single error in the estimation of the principal direction of diffusion can propagate along the trajectory during the tracking process and lead to inaccurate tract reconstructions. The limitations of deterministic tractography algorithms have led to the development of probabilistic methods that introduced the notion of uncertainty in the tractography reconstructions [44].

Probabilistic tractography algorithms use the same tract tracing technique as deterministic methods, but propagate a large number of streamlines chosen from the distribution of possible fiber orientations from a given seed point. Each voxel is then assigned a probability that corresponds to the percentage of streamlines launched from the seed point that pass through that voxel [45–48]. Probability maps provide useful information on the reproducibility of the tracking process, and give an indication of the level of confidence that can be assigned to the existence of a connection between two voxels given the data [27]. The combination of q-ball diffusion models and probabilistic fiber tracking has demonstrated improved sensitivity and predictive power to determine the course of white matter fibers when compared to deterministic approaches [49]. Building on whole-brain probabilistic tractography maps, super-resolution tract density imaging (TDI) can provide elegant depictions of white matter structures beyond the resolution of the diffusion weighted images [50]. However, probabilistic tractography images represent the percentage of tracts that reach a given voxel from the seed point, providing information on the repeatability of the tracking process, but not on the anatomical accuracy of identified pathways. As a result, probabilistic tractography results can be difficult to interpret since a reconstructed tract can be highly reproducible without being anatomically correct [51]. In addition, the choice of the threshold on the percentage of streamlines displayed to select between tract and non-tract voxels remains empirical and is a potential source of variability of the identified pathways.

Both deterministic and probabilistic tractography methods propagate streamlines by considering only directional information at the local level. Numerous ambiguities can occur in regions where multiple fiber populations cross, kiss, or bend, as well as in voxels close to grey matter or within tumoral tissue. Global tractography algorithms have been developed to overcome these limitations by solving a global energy minimization problem [52]. Global tractography methods aim at reconstructing the whole-brain fiber configuration that best explains the measured diffusion-weighted imaging data [53–56]. These sophisticated methods are gaining increasing popularity in the neuroscience community, but their long computation time and the difficulty in specifying prior knowledge criteria have hindered their rapid transfer to the clinics. Recent efforts to make global tractography more practical have demonstrated promising results for clinical applications [57]. Finally, novel filtered tractography algorithms have been introduced to simultaneously estimate a local fiber orientation and perform multi-fiber tractography [58]. These methods have been shown to reduce the diffusion model estimation error and improve the anatomical accuracy of the reconstructed tracts in complex fanning and branching fiber configurations [59]. Studies using a two-tensor filtered tractography technique have demonstrated the feasibility of reconstructing white matter pathways in peritumoral edematous regions [60].

The wide range and diversity of diffusion models and tractography methods developed by the medical image computing community in the last two decades represent a wealth of technical resources to advance knowledge on the architecture of white matter. The path of scientific discovery is likely to be accelerated through neuroscience research efforts such as the Human Connectome Project funded by the U.S. National Institutes of Health, which provides optimized high angular resolution diffusion-weighted imaging acquisition sequences and sophisticated brain mapping tools [61, 177]. New insights on the connectivity of the human brain hold great promise to help advance clinical treatment of low-grade gliomas. Nevertheless, the numerous factors that influence tractography results, such as the choice of diffusion model, fiber tracking algorithm and parameters, and regions of interest for seeding, can make the interpretation of tractography results challenging. While diffusion MRI tractography enables unprecedented visualization of the location and trajectory of white matter fascicles at the individual patient scale, the tracts remain an indirect representation of the underlying white matter anatomy. A solid knowledge of neuroanatomy and an understanding of the current technical limitations of the different methods are essential for the correct interpretation of diffusion MRI tractography reconstructions.

The goal of brain tumor surgery is to maximize tumor resection while preserving eloquent cortical structures and associated subcortical white matter pathways. The extent of surgical resection of diffuse low-grade gliomas (DLGG) has a direct impact on progression free survival, malignant transformation and overall survival [178, 179]. Knowledge of the spatial relationship between the tumor and white matter pathways is critical for two reasons: first, any injury to white matter pathways can lead to permanent neurological deficit of the patient; and second, studies have shown that white matter bundles define the functional limits of surgical resection [62].

Pre-operative T1-weighted, T2-weighted and FLAIR MRI scans are an essential components of neurosurgical planning of brain tumor resection. However, conventional MRI presents some limitations in the depiction of the tumor margins and the relationship between the brain and the disease. Studies have shown that conventional MRI underestimates the extent of DLGG as the tumor cells invade beyond the margins visible on the scans [25, 63]. In addition, tumor cells migrate along white matter pathways, and conventional MRI data lack sufficient contrast to infer the architecture of the brain white matter. In that context, diffusion-weighted MRI and tractography reconstruction are promising tools to help infer the relationship between DLGG and white matter pathways.

Tractography reconstructions can provide three-dimensional visualization of the trajectory and integrity of white matter pathways involved in motor, vision and language function. When combined with functional information from pre-operative functional MRI (fMRI) and intra-operative direct electrical stimulation (DES), tractography has the potential to help understand the anatomo-functional connectivity of the brain at the individual patient scale. The following section introduces the current capabilities and limitations of tractography tools for delineating pathways associated with essential function for the individual management of DLGG.